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#495 aababbaba=babaa

Original presentation

\( \left\langle a, b \;\middle|\; a^{2} b a b^{2} a b a = b a b a^{2} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d, e \;\middle|\; d c a = e a,\; c = a b,\; d = a c^{2} b,\; e = b c a \right\rangle \)

Complete rewriting system

Using recursive path order (RPOCmp) with \(c < d < a < e < b\):

\( \begin{aligned} b c a &\rightarrow e \\ e a &\rightarrow d c a \\ a b &\rightarrow c \\ a c^{2} b &\rightarrow d \\ b c^{2} &\rightarrow e b \\ a e &\rightarrow c^{2} a \\ a c^{2} e &\rightarrow d c a \\ e c &\rightarrow d c^{2} \\ e d &\rightarrow d c d \\ b c d &\rightarrow d c^{3} b \\ a d c a &\rightarrow c^{2} a^{2} \\ a d c d &\rightarrow c^{2} a d \\ a d c^{2} &\rightarrow c^{2} a c \\ a c^{2} d c a &\rightarrow d c a^{2} \\ a c^{2} d c d &\rightarrow d c a d \\ a c^{2} d c^{2} &\rightarrow d c a c \end{aligned} \)